Question

how will you connect three resistance or 2,3and 5 ampere so as to obtain a resultant resistance of 2.5 ampere? draw the diagram to show the arrangement


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Answer 1

Question correction:

Resistors are measured in ohms but not in amperes as mentioned above

Answer:

2 and 3 in series and 5 in parallel to both of them

Explanation:

Given:

Resistance of resistor 1 : 2 ohms

Resistance of resistor 2: 3 ohms

Resistance of resistor 3: 5 ohms

Equivalent resistance: 2.5 ohms

This can be achieved by connecting the 2 and 3 ohms resistor in series

Check:

2 and 3 in series = 2+3 = 5 ohms

5 ohms and 5 ohms in parallel = $\frac{1}{R}=\frac{1}{5}+\frac{1}{5}$

$\frac{1}{R}=\frac{2}{5}$

$R=\frac{5}{2}$

$R=2.5 \ ohms$

Refer to the attchment to see the arrangement:

Answer 2

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$\dag$ CORRECT QUESTION :-

How will you connect three resistance or 2, 3 and 5Ω so as to obtain a resultant resistance of 2.5Ω? draw the diagram to show the arrangement .

GIVEN :-

3 resistors with resistance 2Ω, 3Ω and 5Ω respectively.

TO FIND :-

How the resistors need to be connected so as to obtain an equivalent resistance of 2.5Ω.

PRE-REQUISITE :-

In a series connection,

$\displaystyle{\sf{R_{Equivalent}=R_1+R_2+R_2+....+R_n}}$

In a parallel connection,

$\displaystyle{\sf{\frac{1}{R_{Equivalent}} =\frac{1}{R_1}+\frac{1}{R_2} +\frac{1}{R_3}+....+\frac{1}{R_n} }}$

SOLUTION :-

If we connect the resistors with resistance 2Ω and 3Ω in series and then again, the resistor with resistance 5Ω parallel to the other two resistors, then we may obtain an equivalent resistance of 2.5Ω.

Check :-

2Ω + 3Ω = R      (In series)

⇒R = 5Ω

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Again,

1/R = 1/5 + 1/5    (In parallel)

⇒1/R = 2/5

⇒R = 5/2

⇒R = 2.5Ω

∴ Thus, we finally obtain a resultant resistance of 2.5Ω.

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